Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
398 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C131 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C131 |
| prime radical | #3245×C131 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C22×C4×C131 ◁ C2×C4⋊C8×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2185×C131 | C2 | semidirect |
| 3. #2056×C131 | C2 | semidirect |
| 4. #1347×C131 | C2 | semidirect |
| 5. #1322×C131 | C2 | semidirect |
| 109. C2×C4×C131 | SD32 | semidirect |
| 136. #12161 | C131 | direct (N × H) |
| 137. C131 | #12161 | direct (N × H) |
| 139. #2185 | C2×C131 | semidirect |
| 140. #2056 | C2×C131 | semidirect |
| 141. #1347 | C2×C131 | semidirect |
| 142. #1322 | C2×C131 | semidirect |
| 246. C2×C4 | SD32×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3245×C131 | 2 |
| #2185×C131 | 2 |
| #2056×C131 | 2 |
| #1347×C131 | 2 |
| #1322×C131 | 2 |
| #12161 | 131 |